The development of logical-mathematical reasoning in secondary education showed difficulties related to the understanding of algebraic functions, matrix algebra, and the mastery of prior knowledge. The objective was to analyze the cognitive and pedagogical factors associated with these difficulties among fifth-grade secondary school students in Educational District 08-06 of Santiago, Dominican Republic, and to formulate problem-based instructional guidelines. A quantitative, non-experimental, cross-sectional, descriptive, and correlational study was conducted. The population consisted of 1,850 students and 32 teachers; a stratified probability sample of 318 students was selected, and a census of teachers was conducted. A diagnostic test, structured questionnaires, and an observation guide were administered. The results showed that 68.55% of the students reached an insufficient performance level; the main difficulties were found in conversion between representations, functional modeling, and contextualized solving of matrix systems. Expository teaching predominated, and gaps in prior knowledge were negatively associated with mathematical reasoning. The instructional proposal received a favorable feasibility assessment. These findings suggested a relationship among conceptual gaps, teacher mediation, and performance. It was concluded that prior knowledge leveling should be articulated with problem-based learning.
The development of logical-mathematical reasoning in secondary education showed difficulties related to the understanding of algebraic functions, matrix algebra, and the mastery of prior knowledge. The objective was to analyze the cognitive and pedagogical factors associated with these difficulties among fifth-grade secondary school students in Educational District 08-06 of Santiago, Dominican Republic, and to formulate problem-based instructional guidelines. A quantitative, non-experimental, cross-sectional, descriptive, and correlational study was conducted. The population consisted of 1,850 students and 32 teachers; a stratified probability sample of 318 students was selected, and a census of teachers was conducted. A diagnostic test, structured questionnaires, and an observation guide were administered. The results showed that 68.55% of the students reached an insufficient performance level; the main difficulties were found in conversion between representations, functional modeling, and contextualized solving of matrix systems. Expository teaching predominated, and gaps in prior knowledge were negatively associated with mathematical reasoning. The instructional proposal received a favorable feasibility assessment. These findings suggested a relationship among conceptual gaps, teacher mediation, and performance. It was concluded that prior knowledge leveling should be articulated with problem-based learning. Read More